If the incident beam is collimated (parallel beam of light )... The FWHM broadening is really negligeable (10-5 in relative value for one degree tilt)...
if we do not have a telecentric system :
the angle of the cones of light are set by the F/D ratio (=> FWHM broadening), but the angle of the axis of the cone of light changes along the field of view => CWL shift along the field of view. It seems that the second effect add an additional FWHM broadening depending of the position in the field of view. I still have to work on that
Hmm... good food for thought. However, it does remind me of and make me wonder if the "sweet spot" found in collimator based systems is due to only CWL/band-pass shifting, or if band-pass broadening also might be at work, and what that would look like... So thinking out loud so to speak:
If we examine the curves you have given for the 0.6 A filter in a collimated beam, it appears we also might encounter band-pass broadening due to field angle magnification. For example, if the collimator focal length is 1/4 the objectives FL, we will have a field angle magnification of 4 x, and the sun's limb field angle will be 0.25 x 4 = 1 degree. We can see in this system the FWHM is blue-shifted by ~ 0.4 A at the limb, with an identical 0.4 A shift at the 10% transmission.
Could "integration of the shift of CWL" of the field angles in the collimator system be contributors to band-pass broadening - just as the suspected broadening that occurs with a telecentric based system are due to the non-normal angles of the F/D light cones? The answer indeed is no, at least for the filter diameter as a whole. This broadening would be the FWHM from the right side of the blue transmission curve to the left side of the green transmission curve or beyond. We would see the decrease in disc contrast due to increased continuum light, but prominences would not be affected, or perhaps become even brighter due to blue Dopper shifiting events. So if prominences remain visible, this would indicate the band-pass was broadened due to the wider band-pass still encompassing the H alpha emission line.
But what we observe for disk features is that more light from the photosphere intrudes and decreases contrast, but for prominences away from the suns disc, the off-axis CWL shift results in the filter eventually going off-band, and prominences disappearing (i.e. the green transmission curve). This is also why minimizing field angle magnification is important in collimator based systems for good overall band-pass/contrast performance.
The differences between collimator verses telecentric systems: OPTIMIZED telecentrics will have a uniform broadening of the filter band-pass across the etalon due to all light cones (e.g. center and limb) having the same intercept angles at the etalon. This broadening is apparently due only to the F/D angles of the light cone -- with the narrower the F/D cone allowing the tighter the band-pass, and why optimizing the F/D ratio is so important the narrower the filter bandpass. Collimator systems are inherently non-uniform in CWL shifting, which is highly dependent on field angle magnifications off-axis presented to the etalon.
However, if we use a non-optimized telecentric system - e.g. a typical barlow, "telecentric barlow," or a proper telecentric used with an incorrect focal length - we might likely get both FWHM broadening and CWL shifting across the etalon, e.g. resulting in a "sweet spot" due to "cone tilt." This again is what I have observed. But of course I could be wrong in my thought analysis...
Addendum: Going back and reviewing the thorough treatise on telecentric performance by Gene Baraff ( http://home.comcast....erving/Tele.pdf ):
In the less-than-ideal situation where design and actual focal lengths differ, the cone axes are tilted. That tilt gives rise to wavelength shift [Equation (21)] and to pass-band broadening [Equation (22)], both of which become worse with distance from the axis... Emphasis added.
Note that in Figure 4 (pg. 18) the cone tilts vary non-linearly with distance from the optical axis, just as CWL shifts do in a collimator based system (seen in your plot of tilt angles):
The shift - towards shorter wavelengths - grows quadratically with distance from the axis. In addition to the shift, there is broadening because of the range of angles striking a given image point.
From Gene's work, it indeed appears that for an un-optimized telecentric system, CWL shift (generating a "sweet spot") is the dominant consequence, with band-pass (and transmission profile) broadening seemingly of secondary significance in the majority of instances, provided the overall F/D ratio is already optimized.
Edited by BYoesle, 19 January 2015 - 08:32 AM.